Binary tensor train Gröbner basis conjecture

Let $\mathbf{k}=(2)_{n+1}$ and $\mathbf{r}=(1,r_2,\dots,r_{n-1},1)$. For each $i$, let $G_i^{(r_i+1)}$ denote the set of $(r_i+1)$-minors of the flattening $\psi^{i-1}$, and let $\mathcal I(V_{\mathbf{k},\mathbf{r}})$ be the ideal of the corresponding tensor train variety. Binary tensor train Gröbner basis conjecture. The union

$$G^{(r_1+1)}_1\cup\cdots\cup G^{(r_n+1)}_n$$

of these minors forms a Gröbner basis of $\mathcal I(V_{\mathbf{k},\mathbf{r}})$ with respect to the reverse-lexicographic order induced by a variable order compatible with the flattenings. This is presented as a key step toward the determinantal ideal conjecture; the statement is supported by positive evidence for binary tensors but remains open.